Related papers: Probabilistic multi-Stirling numbers of the second…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, probabilistic Stirling numbers of the first kind and of the second kind associated with Y have been introduced. However,…
Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. We study the probabilistic degenerate r-Stirling numbers of the second kind associated with Y and the probabilistic degenerate…
In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. The aim of this paper is to…
Let Y be a random variable whose moment-generating function exists in some neighborhood of the origin. While probabilistic Stirling numbers of the first and second kind have been introduced, early definitions often failed to satisfy…
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
The multi-Stirling numbers of the second kind, the unsigned multi-Stirling numbers of the first kind, the multi-Lah numbers and the multi-Bernoulli numbers are all defined with the help of the multiple logarithm, and generalize respectively…
Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are…
Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. The aim of this paper is to study the probabilistic Lah numbers associated with Y and the probabilistic Lah-Bell polynomials associated…
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the…
In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
The aim of this paper is to study probabilistic versions of the degenerate Whitney numbers of the second kind and those of the degenerate Dowling polynomials, namely the probabilistic degenerate Whitney numbers of the second kind associated…
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…
We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these…
Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated…
Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the derangement polynomials, the derangement polynomials of type 2…
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate $r$-Stirling numbers of the second kind, the degenerate Stirling…
The author has constructed multiple analogues of several families of combinatorial numbers in a recent article, including the bracket symbol, and the Stirling numbers of the first and second kind. In the present paper, a multiple analogue…
We introduce multinomial and $r$-variants of several classic objects of combinatorial probability, such as the random recursive and Hoppe trees, random set partitions and compositions, the Chinese restaurant process, Feller's coupling, and…